Solve frac{3^frac{4{5}}*3^frac{2{3}}}{3^-frac{1{5}}*3^-frac{1{3}}}

$$\frac { 3 ^ { \frac { 4 } { 5 } } * 3 ^ { \frac { 2 } { 3 } } } { 3 ^ { - \frac { 1 } { 5 } } \times 3 ^ { - \frac { 1 } { 3 } } }$$

Evaluate

$$9$$

Solution Steps

To multiply powers of the same base, add their exponents. Add \frac{4}{5} and \frac{2}{3} to get \frac{22}{15}.

$$\frac{3^{\frac{22}{15}}}{3^{-\frac{1}{5}}\times 3^{-\frac{1}{3}}}$$

To multiply powers of the same base, add their exponents. Add -\frac{1}{5} and -\frac{1}{3} to get -\frac{8}{15}.

$$\frac{3^{\frac{22}{15}}}{3^{-\frac{8}{15}}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -\frac{8}{15} from \frac{22}{15} to get 2.

$$3^{2}$$

Calculate 3 to the power of 2 and get 9.

$$9$$

Factor

$$3^{2}$$